By A. A. Ivanov

This publication is the 1st quantity in a two-volume set, to be able to give you the whole evidence of type of 2 very important sessions of geometries, heavily regarding one another: Petersen and tilde geometries. there's an unlimited family members of tilde geometries linked to non-split extensions of symplectic teams over a box of 2 components. in addition to that there are twelve extraordinary Petersen and tilde geometries. those unparalleled geometries are on the topic of sporadic uncomplicated teams, together with the recognized Monster team and this quantity offers a building for every of the Petersen and tilde geometries which gives an autonomous lifestyles evidence for the corresponding automorphism crew. very important purposes of Petersen and Tilde geometries are thought of, together with the so-called Y-presentations for the Monster and comparable teams, and an entire indentification of Y-groups is given. this can be a necessary buy for researchers into finite staff concept, finite geometries and algebraic combinatorics.

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